Question

the root of x3 - 2x -5 = 0 correct to three decimal places by using newton raphson method is options. 2.0946,1.0404 ,1.7321,0.701 answer​

Answer 1

Given : x³ - 2x - 5=0

 To Find : one root by  by Newton-Raphson Method

correct 4 decimal  

 

Solution:

f(x) =   x³ - 2x - 5

f'(x) = 3x² - 2

x₀  = 2  

xₙ₊₁  = xₙ ​−f(xₙ​)​./ f′(xₙ​)

x₁  = 2 -  (2³ - 2*2- 5)/  (3*2² - 2)

x₁  =  2 -  (-1)/10

x₁  = 2.1

x₂ = 2.1 -  (2.1³ - 2*2.1- 5)/  (3*2.1² - 2)

=> x₂ = 2.09457

x₃ =  2.09455  

x₄ = 2.09455

2.09455

hence x = 2.0946  upto 4 decimal  places

Learn More:

Evaluate √30 to four decimal places by using Newton-Raphson ...

brainly.in/question/17089871

Evaluate √167 by Newton Raphson method correct up to four ...

brainly.in/question/18159565